c-Nilpotent Multiplier of Finite p-Groups

The aim of this work is to find some exact sequences on the c-nilpotent multiplier of a group G. We also give an upper bound for the c-nilpotent multiplier of finite p-groups and give the explicit structure of groups whose take the upper bound. Finally, we will get the exact structure of the c-nilpotent multiplier and determine c-capable groups in the class of extra-special and generalized extra-special p-groups. It lets us to have a vast improvement over the last results on this topic.